Drinfeld category and the classification of singular Gelfand-Tsetlin -modules

Author(s)

Futorny, Vyacheslav ^[1] ; Grantcharov, Dimitar ^[2] ; Ramirez, Luis Enrique ^[3]

Affiliation

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

^[2] Univ Texas Arlington, Arlington, TX 76019 - USA

^[3] Univ Fed ABC, BR-09210580 Santo Andre, SP - Brazil

• Document type: Journal article
• Source: INTERNATIONAL MATHEMATICS RESEARCH NOTICES; v. 2019, n. 5, p. 1463-1478, MAR 2019.
• Web of Science Citations: 1

Abstract

We prove a uniqueness theorem for irreducible non-critical Gelfand-Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand-Tsetlin modules with -singularity. An explicit construction of such modules was given in Futorny et al. {[}7]. In particular, we show that the modules constructed in Futorny et al. {[}7] exhaust all irreducible Gelfand-Tsetlin modules with -singularity. To prove the result, we introduce a new category of modules (called Drinfeld category) related to the Drinfeld generators of the Yangian and define a functor from the category of non-critical Gelfand-Tsetlin modules to the Drinfeld category. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants